Abstract
We study the broadcast message complexity of secure multiparty computation (MPC), namely, the total number of messages that are required for securely computing any functionality in the broadcast model of communication.
MPC protocols are traditionally designed in the simultaneous broadcast model, where each round consists of every party broadcasting a message to the other parties. We show that this method of communication is sub-optimal; specifically, by eliminating simultaneity, it is, in fact, possible to reduce the broadcast message complexity of MPC.
More specifically, we establish tight lower and upper bounds on the broadcast message complexity of n-party MPC for every \(t<n\) corruption threshold, both in the plain model as well as common setup models. For example, our results show that the optimal broadcast message complexity of semi-honest MPC can be much lower than 2n, but necessarily requires at least three rounds of communication. We also extend our results to the malicious setting in setup models.
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Notes
- 1.
Recall that the messages sent by honest parties in any round are independent of each other.
- 2.
When \(n=2t+1\), this is the same as guaranteed output delivery. However, for \(n>2t+1\), this is a strengthening of guaranteed output delivery.
- 3.
If multiple parties speak in the same round in \(\varPi \), they can be arranged in any order.
- 4.
In the case of \(|{\mathcal O} |=1\), we simply add the output party as the last node on the chain. With this approach, we obtain a protocol with P2P message complexity k, starting from a protocol with broadcast message complexity k. For the case of \(|{\mathcal O} |=n\), we can actually do better, and simply delete the last message (since the last node on the chain can compute it on its own), resulting in a protocol with P2P message complexity \(k-1\).
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Acknowledgments
The first author is supported in part from DARPA/ARL SAFEWARE Award W911NF15C0210, AFOSR Award FA9550-15-1-0274, AFOSR Award FA9550-19-1-0200, AFOSR YIP Award, NSF CNS Award 1936826, DARPA and SPAWAR under contract N66001-15-C-4065, a Hellman Award and research grants by the Okawa Foundation, Visa Inc., and Center for Long-Term Cybersecurity (CLTC, UC Berkeley). The second and third authors are supported in part by NSF SaTC grant 1814919 and Darpa Safeware grant W911NF-15-C-0213. The views expressed are those of the authors and do not reflect the official policy or position of the funding agencies.
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Garg, S., Goel, A., Jain, A. (2019). The Broadcast Message Complexity of Secure Multiparty Computation. In: Galbraith, S., Moriai, S. (eds) Advances in Cryptology – ASIACRYPT 2019. ASIACRYPT 2019. Lecture Notes in Computer Science(), vol 11921. Springer, Cham. https://doi.org/10.1007/978-3-030-34578-5_16
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